The metric results of [1]}, [2]} and Euclidean results of [1]}, [4]}, [5]}, [2]} that rely on merge-and-reduce have already been mentioned. A summary of these results appears in the tables below.
For the specific case of Euclidean space, a more diverse set of stronger results is known. In particular, coreset constructions are known that do not begin with a bicriterion solution, and whose streaming variant does not rely on merge-and-reduce [7]}.
With the additional assumption in Euclidean space that the points lie on a discrete grid \(\lbrace 1,\ldots ,\Delta \rbrace ^d\) , alternative techniques are known for \(k\) -means and other problems, even when the stream allows the deletion of points [8]}.
